Default Risk, Shareholder Advantage, and Stock Returns

Transcription

1 Default Risk, Shareholder Advantage, and Stock Returns Lorenzo Garlappi University of Texas at Austin Tao Shu University of Texas at Austin Hong Yan University of Texas at Austin and SEC First draft: March 2005 This draft: July 2006 We are grateful to Moody s KMV for providing us with the data on Expected Default Frequency (EDF ) and to Jeff Bohn and Shisheng Qu of Moody s KMV for help with the data and for insightful suggestions. We appreciate useful comments and suggestions from Jonathan Berk, Jason Chen, Kent Daniel, Sanjiv Das, Sergei Davydenko, Mara Faccio, Andras Fulop, Raymond Kan, Hayne Leland, Mahendrarajah Nimalendran, Burton Hollifield, George Oldfield, Hernan Ortiz-Molina, Ramesh Rao, Jacob Sagi, Matthew Spiegel (the editor), Sheridan Titman, Stathis Tompaidis, Raman Uppal, two anonymous referees, and seminar participants at George Washington University, Hong Kong University of Science and Technology, University of California at Berkeley, University of Hong Kong, University of Lausanne, University of South Carolina, University of Texas at Austin, University of Toronto, University of Vienna, the Eighth Texas Finance Festival, the Third UBC Summer Conference, the Third Moody s NYU Credit Risk Conference and the 2006 Festkolloquium in honor of Phelim Boyle. We are responsible for all errors in the paper. The U.S. Securities and Exchange Commission disclaims responsibility for any private publication or statement of any SEC employee. This study expresses the authors views and does not necessarily reflect those of the Commission, the Commissioners, or other members of the staff. McCombs School of Business, B6600, The University of Texas at Austin, Austin TX, lorenzo.garlappi@mccombs.utexas.edu McCombs School of Business, B6600, The University of Texas at Austin, Austin TX, tao.shu@phd.mccombs.utexas.edu U.S. Securities & Exchange Commission, Office of Economic Analysis, 100 F Street, N.E., Washington, DC yanh@sec.gov

2 Default Risk, Shareholder Advantage, and Stock Returns Abstract In this paper, we study the relationship between default probability and stock returns. Using the market-based measure of Expected Default Frequency (EDF ) constructed by Moody s KMV, we first demonstrate that higher default probabilities are not necessarily associated with higher expected stock returns, a finding that complements the existing empirical evidence. Adapting the setting of the Fan and Sundaresan (2000) model that explicitly considers the bargaining game between equity-holders and debt-holders of a firm in financial distress, we obtain a theoretical relationship between expected returns and default probability that resembles the empirically observed pattern. Our analysis indicates that the relationship between default probability and equity return tends to be (i) upward sloping for firms where shareholders are not likely to extract significant benefits from renegotiation (low shareholder advantage ) and (ii) humped and downward sloping for firms where shareholder advantage is strong. Moreover, this divergence in the relationship implies that distressed firms in which shareholders have a stronger advantage in renegotiation exhibit lower expected returns. We test these implications using several proxies for shareholder advantage and find results that are consistent with the model s predictions. Keywords: Default Risk, Stock Returns, Debt Renegotiation, Bankruptcy, Liquidation. JEL Classification Codes: G12, G14.

3 1 Introduction Default risk usually refers to the likelihood that a levered firm will not be able to pay the contractual interest or principal on its debt obligations. Several studies have argued for a role of default risk in explaining some of the anomalies in the cross section of equity returns. The argument proposed by these studies rests on the conjecture that investors demand a positive premium for holding stocks of firms that face a high probability of default. 1 Using various measures of the probability of default, the existing empirical literature has not produced consistent evidence to confirm the above conjecture. In fact, some studies have documented the opposite result, i.e., stocks of companies with a higher probability of default usually earn lower returns. 2 A prevalent interpretation of this empirical evidence is one of market mispricing, namely, investors are incapable of fully assessing the prospects of firms with high default probabilities and hence fail to demand a sufficient premium to compensate for the risk of default. In this paper, we propose an economic mechanism that helps reconcile the conflicting interpretations of the link between returns and default probability. This mechanism relies on the effects of strategic interactions between equity holders and debt holders on equity returns. Our theoretical analysis and empirical evidence indicate that shareholder advantage, i.e., the ability of shareholders to extract rents from their interactions with other claimholders, has a direct impact on the equity risk of firms with high default probability and helps account for much of the observed cross-sectional variations in the relationship between default probability and stock returns, above and beyond the known effects of size, book-to-market ratio and momentum. 1 For instance, Chan, Chen, and Hsieh (1985) show that a default factor constructed as the difference between high- and low- grade bond return can explain a large part of the size effect. Fama and French (1992) and Chen, Roll, and Ross (1986) document the power of a similarly defined default factor in explaining the cross section of stock returns. Chan and Chen (1991) justify the role of distress risk by arguing that the size premium is primarily driven by marginal firms, i.e., firms with low market value, cash flow problems, and high leverage that are more sensitive to adverse economic fluctuations. Fama and French (1992) also link the book-to-market effect to the risk of distress. Moreover, Fama and French (1996) suggest that, if distress events are correlated across firms, a firm s relative distress can act as a state variable affecting investors human capital and ultimately asset prices in the cross section. More recently, Vassalou and Xing (2004) argue that default risk is positively priced in the market and is associated with both size and value effects. 2 Using both Altman (1968) Z-score and Ohlson (1980) O-score, Dichev (1998) documents a negative relationship between stock return and default probability. Griffin and Lemmon (2002) find that this pattern is stronger for firms with low book-to-market ratios. More recently, this pattern has been confirmed by Campbell, Hilscher, and Szilagyi (2005) using a hazard model to predict default probability. Furthermore, Avramov, Chordia, Jostova, and Philipov (2005) link momentum returns to credit deterioration.

4 2 We carry out our study in three steps. First, we revisit the empirical relationship between default probability and stock returns by directly employing a database of Expected Default Frequencies (EDF ) produced by Moody s KMV, which is widely used by financial institutions as a predictor of default probability. Using the EDF measure, we find that higher default probabilities do not consistently lead to higher expected stock returns. In particular, small firms and/or firms with low-priced stocks exhibit different behavior than large firms. While this finding complements the existing evidence, it is also suggestive of cross-sectional variations in the relationship. Second, we show that the assessment of equity risk of default should take into account the potential recovery for shareholders, which is an outcome of the renegotiation between claimholders in the event of financial distress. While a number of theoretical models have explicitly considered this strategic interaction in the context of optimal capital structure and credit spreads on corporate bonds, 3 to the best of our knowledge, our study is the first to show that this consideration is also important for explaining the puzzling behavior of stock returns. For this purpose, we adapt the model of Fan and Sundaresan (2000), whose parsimonious setup captures the essence of the bargaining game between debt-holders and shareholders and allows us to derive explicitly the link between default probability and expected stock returns. Our analysis highlights the crucial role of shareholder advantage defined as the combination of shareholders bargaining power and the efficiency gained through bargaining in the determination of equity returns. 4 We show that, within the context of the above model, the ability of shareholders with a stronger advantage to extract more value from renegotiation leads to lower risk for equity relative to the risk of the assets and hence lower expected returns, as the probability of default increases. On the other hand, for firms whose shareholders have a weak advantage, the model predicts a positive relationship between default probability and expected equity returns, consistent with the original intuition that default risk should be compensated 3 See, for example, Anderson and Sundaresan (1996), Mella-Barral and Perraudin (1997), Fan and Sundaresan (2000), Acharya, Huang, Subrahmanyam, and Sundaram (2004), and François and Morellec (2004). 4 Shareholder advantage is best represented by the violation of the absolute priority rule (APR) during bankruptcy proceedings. However, in other instances of default, such as private workouts, where the absolute priority rule is not clearly defined, our concept of shareholder advantage still applies.

5 3 by a positive return premium. Our analysis indicates that, in the presence of shareholder advantage, default probability does not adequately represent the risk of default to equity, since higher default probability is also associated with a potential reduction in debt burden and hence in equity risk. In fact, the trade-off between the risk of default to equity and the likelihood of bargaining gains in renegotiation results in a hump-shaped relationship between expected returns and default probability. Third, through the lens of our theoretical analysis, we take a fresher look at the data. We hypothesize that the negative relationship between default probability and expected returns is more pronounced for firms with (i) a large asset base, which can make their shareholders more powerful in renegotiations; (ii) low R&D expenditures, which, ceteris paribus, reduce the likelihood of a liquidity shortage and hence strengthen shareholders bargaining position; and (iii) high liquidation costs proxied by asset specificity which give debt-holders a strong incentive for a negotiated settlement. On the other hand, the relationship turns positive for firms at the opposite extreme of these variables. Using these variables as proxies for shareholder advantage, we test our hypotheses through both a sub-portfolio analysis and a multivariate regression analysis. Our empirical findings are consistent with the model s conjecture about the key role of shareholder advantage in determining the link between default probability and stock returns. In particular, returns decrease in EDF for firms with (i) large asset size and low R&D expenditure (proxies for high bargaining power) and (ii) high asset specificity i.e., in a concentrated industry or with low asset tangibility (proxies for high bargaining surplus). Moreover, we find that the cross-sectional divergence in the relationship for firms with strong versus weak shareholder advantage is both statistically significant and economically meaningful. There is a large body of work devoted to modelling default risk for valuing corporate debt, compared to the relatively thin literature on the link between default probability and stock returns. 5 Several recent theoretical papers also examine specific features of bankruptcy codes 5 See Duffie and Singleton (2003) for a comprehensive overview of the literature on credit risk and the pricing of corporate debt.

6 4 and their effects on the valuation of corporate debt. 6 None of these papers, however, focus on the relationship between stock returns and default probability examined in this paper. On the empirical side, Davydenko and Strebulaev (2006) investigate the significance of shareholders strategic actions for credit spreads and find that while the effect is statistically significant, its economic impact on credit spreads is minimal. In this paper we show that, conversely, the economic impact of shareholders strategic actions can be very significant to shareholders, who would have received nothing in liquidation. Our study demonstrates that this economic mechanism can help explain the complex effect of default risk on stock returns and highlights the importance of strategic interactions in a setting where it matters the most to the residual claimants. The rest of the paper proceeds as follows. In Section 2, we review the existing empirical evidence on the relationship between default probability and stock returns and present our own empirical results. In Section 3, we explicitly derive the relationship between returns and default probability in the context of the Fan and Sundaresan (2000) model, and in Section 4 we test its empirical implications in the cross section. We conclude in Section 5. We provide technical details and describe the model simulation procedure in the Appendix. 2 Default probability and stock returns: empirical evidence In this section, we first review the previous evidence in the literature on the relationship between stock returns and default probability. We then report the results of our own preliminary empirical investigation relying on the market-based measures of default probability obtained from Moody s KMV (MKMV hereafter). 6 See, for example, Broadie, Chernov, and Sundaresan (2004), Galai, Raviv, and Wiener (2003), François and Morellec (2004), and Paseka (2003). Alternatively, Von Kalckreuth (2005) proposes an explanation based on non-financial reward from corporate control.

7 5 2.1 Previous empirical evidence Using Ohlson s (1980) O-score and Altman s (1968) Z-score to proxy for the likelihood of default, Dichev (1998) documents an inverse relationship between stock returns and default probability. 7 This result is confirmed by Griffin and Lemmon (2002), who argue that the phenomenon is driven by the poor performance of the firms with low book-to-market ratio and high distress risk, and attribute it to market mispricing of these stocks. Campbell, Hilscher, and Szilagyi (2005) study the determinants of corporate bankruptcy using a hazard model approach, similar to that in Shumway (2001) and Chava and Jarrow (2002). Using the resulting forecast measure of default probability, they also find that firms with a high probability of bankruptcy tend to earn low average returns and suggest that this evidence is indicative of equity markets mispricing distress risk. Hillegeist, Keating, Cram, and Lundstedt (2004) show that both O-score and Z-score are limited in their forecasting power and advocate the use of a measure based on the Black and Scholes (1973) and Merton (1974) option pricing framework, similar to the EDF measure provided commercially by MKMV. Vassalou and Xing (2004) construct a metric for default probability to mimic the EDF measure. They find that high-default-probability firms with a small market capitalization and a high book-to-market ratio earn higher returns than their low-default-probability counterparts and conclude that default risk is systematic and positively priced in stock returns. This result is contrary to the other evidence in the literature and has been challenged on the ground of return attribution. 8 In the remainder of this section, we present our own evidence on the relationship between stock returns and default probability using a measure of default likelihood that relies on information included in market prices. 7 There is, however, a discernable hump in the relationship documented by Dichev (1998), which is not discussed in the paper. 8 Da and Gao (2005) argue that some of the very high returns earned by small stocks with high default risk and a high book-to-market ratio are attributable to the illiquidity of these stocks.

8 6 2.2 Our empirical findings Data and summary statistics In our empirical investigation we use the Expected Default Frequency (EDF) obtained directly from MKMV. This measure is constructed from the Vasicek-Kealhofer model (Kealhofer (2003a,b)), which adapts the contingent-claim framework of Black and Scholes (1973) and Merton (1974) to make it suitable for practical analysis. 9 To be included in our analysis using the EDF measure, a stock needs to be present simultaneously in the CRSP, COMPUSTAT, and MKMV databases. Specifically, for a given month, we require a firm to have an EDF measure and an implied asset value in the MKMV dataset; price, shares outstanding and returns data from CRSP; and accounting numbers from COMPUSTAT. We limit our sample to non-financial U.S. firms. 10 We drop from our sample stocks with a negative book-to-market ratio. Our baseline sample contains 1,430,713 firm-month observations and spans from January 1969 to December Summary statistics for the EDF measure are reported in Table 1. The average EDF measure in our sample is 3.44% with a median of 1.19%. 12 The table shows that there are time-series variations in the average as well as in the distribution of the EDF measure, and that the majority of the firms in our dataset have an EDF score below 4%. Since the EDF measure is based on market prices, in order to mitigate the effect of noisy stock prices on the default score, we use an exponentially smoothed version of the EDF measure, based on a time-weighted average. Specifically, for default probability in month t, we use EDF t = 5s=0 e sν EDF t s 5s=0 e sν, (1) 9 See Crosbie and Bohn (2003) for details on how MKMV implements the Vasicek-Kealhofer model to construct the EDF measure. In addition, as indicated by Moody s KMV, the EDF measure is constructed based on extensive data filtering to avoid the influence of outliers due to data errors, a sophisticated iterative search routine to determine asset volatility and access to a comprehensive database of default experiences for an empirical distribution of distance-to-default. 10 Financial firms are identified as firms whose industrial codes (SIC) are between 6000 and We follow Shumway (1997) to deal with the problem of delisted firms. Specifically, whenever available, we use the delisted return reported in the CRSP datafile for stocks that are delisted in a particular month. If the delisting return is missing but the CRSP datafile reports a performance-related delisting code (500, ), then we impute a delisted return of 30% in the delisting month. 12 MKMV assigns an EDF score of 20% to all firms with an EDF measure larger than 20%.

9 7 where ν is chosen to satisfy e 5ν = 1/2, such that the five-month lagged EDF measure receives half the weight of the current EDF measure. The empirical results are reported based on EDF t, which we will still refer to as EDF for notational convenience. Our results, however, are robust to the use of the original EDF measure Equity returns and default probability In this section we analyze the relationship between equity returns and default probability measured by EDF. As Table 1 illustrates, the EDF measure exhibits substantial variation over time. The time variation in the EDF score can cause problems if we want to compare the cross-sectional relationship between default probability and returns in different time periods. To avoid such problems, when linking returns to default probabilities we use the EDF rank in the cross section, instead of the EDF score itself. Because the EDF measure is based on equity prices, there is a natural concern about a spurious relationship between EDF and stock returns. Several considerations can help alleviate this concern. First, the time-weighted EDF measure is not contemporaneous with the stock price as it is exponentially weighted through time. Second, our use of the ranking of EDF will mitigate any potentially mechanical link between EDF and returns. Third, since in all our empirical tests we control for return momentum, the possibility of a spurious correlation between EDF and returns is further reduced. We start our analysis by forming portfolios of stocks according to each firm s EDF rank in month t. We then analyze the returns of these portfolios in month t + 2, i.e., we skip a month between portfolio formation and return recording. There are two reasons for this choice. First, as suggested by Da and Gao (2005), skipping a month is important to alleviate the microstructure issues that notoriously affect low-priced firms near default. 13 Second, skipping a month helps further alleviate the concern of detecting a spurious relationship between EDF and returns. The results are presented in Table 2 where we report equally- and value-weighted portfolio returns when using both the full sample of stocks (Panel A) and the subsample of stocks with a 13 We also repeat our analysis with quarterly, instead of monthly, returns and obtain qualitatively similar results.

10 8 price per share higher than two dollars (Panel B). To isolate the effect of the EDF measure on stock returns from other characteristics known to affect stock returns, we follow the methodology suggested by Daniel, Grinblatt, Titman, and Wermers (1997) (DGTW henceforth) and adjust the return of each stock by subtracting the return of a benchmark portfolio that matches the stock s size, book-to-market ratio, and momentum (see also Wermers (2004)). 14 The sample period of DGTW-adjusted returns spans from June 1975 to June 2003 due to the availability of the benchmark portfolio returns. The adjusted returns are reported under the label DGTW returns in both panels of Table 2. The first two rows of Panel A (full sample) demonstrate an intriguing pattern in the relationship between raw stock returns and measures of default probability. While equally-weighted portfolio returns are positively related to default probability, for value-weighted portfolio returns, this relationship is almost flat and slightly humped. With DGTW-adjusted returns, Panel A in Table 2 shows that the relationship for equally-weighted returns is now strongly positive and statistically significant, while the relationship for value-weighted returns remains mostly flat and slightly humped. The difference in the behavior of equally- and value-weighted portfolio returns is statistically significant both for raw returns and for DGTW-adjusted returns. The difference between value- and equally-weighted returns is traditionally argued to be caused by the size effect. If the size effect is the only cause for this difference, then it should disappear in DGTW-adjusted returns. The fact that this difference persists and is even more significant with DGTW-adjusted returns suggests an additional effect that might be related to the size of a firm. The results for both equally- and value-weighted portfolios with raw returns are similar to those obtained by Vassalou and Xing (2004), who use their own EDF-mimicking measure for default likelihood. 15 Vassalou and Xing (2004) claim that the pattern associated with the equally-weighted returns is indicative of positively priced default risk and dismiss the previous 14 We thank Kent Daniel and Russ Wermers for providing data on the benchmark portfolio returns. 15 While Vassalou and Xing (2004) construct their own market-based default probability measure using the Merton (1974) model, we use the EDF measure directly obtained from MKMV. Because results can be heavily impacted by outliers in these measures due to data errors, by using MKMV s EDF measure directly we benefit from the extensive data cleaning and the rich empirical default database reflected in MKMV s EDF measure.

11 9 evidence of a negative association between stock returns and default probability as a result of imperfect, accounting-based measures of default likelihood. However, the distinct behavior of value- and equally-weighted portfolios reported in Panel A of Table 2 suggests caution in drawing conclusions concerning how default risk is priced. To see the impact of extremely low-priced stocks on this return pattern, we report in Panel B the results obtained by excluding stocks with a price per share less than two dollars. The absence of low-priced stocks takes away the positive relationship between equally-weighted returns and EDF while keeping the result for value-weighted returns qualitatively similar. The difference between equally- and value-weighted returns is no longer statistically significant for DGTW returns, confirming the conjecture that the positive relationship for equally-weighted returns in Panel A is attributable to low-priced stocks. Compared with the results for the full sample in Panel A, this finding suggests that the DGTW correction for size/book-to-market/momentum works quite well for stocks in the subsample of stocks with a price greater than two dollars but fails to account for those low-priced stocks. Since stocks in distress are more likely to have low prices, these results imply that the effect of default is not subsumed by size, book-to-market ratio, and momentum. To understand these potential cross-sectional variations in the relationship between equity returns and default probability, it is necessary to take a closer look at the microeconomic forces at play for firms facing financial distress. In the next section, we propose a plausible economic mechanism that produces predictions consistent with the patterns we observe in the data. 3 Default probability and stock returns: a theoretical model The Merton (1974) model characterizes equity as a call option on the firm s assets and implicitly assumes that default equals liquidation. In reality, liquidation is only one of the possibilities open to a firm in financial distress, and it is usually a choice of the last resort. Frequently, firms choose to renegotiate outstanding debt either in a private workout or under the protection of the U.S. Bankruptcy Code (Chapter 11). Frequently, bankruptcy procedures allow for opportunistic behavior of claimholders and subsequent violation of the absolute priority rule (e.g., Franks and

12 10 Torous (1989), Weiss (1991), Eberhart, Moore, and Roenfeldt (1990), and Betker (1995)). In an attempt to understand the relationship between capital structure decision and debt pricing, Anderson and Sundaresan (1996), Mella-Barral and Perraudin (1997), Fan and Sundaresan (2000), Acharya, Huang, Subrahmanyam, and Sundaram (2004) explicitly evaluate corporate claims within a model that allows for out-of-court renegotiations, while François and Morellec (2004) develop a model to capture the unique features of Chapter 11 renegotiation (automatic stay and exclusivity period). 16 In this section, we show how the strategic framework proposed by these theoretical models can be used to provide insights into the puzzling empirical relationship between default probability and stock returns documented earlier. The main intuition is that allowing for renegotiation provides room for strategic default, and shareholders can extract rents in the form of lower or deferred payments on their debt obligations in the process. This shareholder advantage is a function of their bargaining power and affects the riskiness of equity. The stronger shareholders advantage in renegotiation is, the higher their rent extraction ability is, and the lower the risk and expected return of equity are. We analyze the connection between default probability and return to equity by adapting the model of Fan and Sundaresan (2000), originally designed to study the implication of the relative bargaining power of claimants on optimal reorganization and debt valuation (p. 1050, their emphasis). As it will become clear, the implication of our analysis can also be obtained in the context of other models that allow for a bargaining game in renegotiation. 3.1 A model of strategic debt service We first briefly review the basic elements of the renegotiation model of Fan and Sundaresan (2000) (FS hereafter). The model is set in continuous time and considers a firm which issues a single tranche of perpetual debt with a promised coupon c per unit time. The payment of the contractual coupon entails the firm to a tax benefit τc (0 τ 1) that is lost during the 16 Other papers analyzing the effect of the bankruptcy codes on debt valuation include Acharya, Sundaram, and John (2005), Broadie, Chernov, and Sundaresan (2004), Galai, Raviv, and Wiener (2003), and Paseka (2003).

13 11 default period. There are dissipative liquidation costs, measured as a fraction α of the value of the assets upon liquidation, where equity-holders get nothing and debt-holders get a fraction (1 α) of the firm s assets. 17 The asset value of the firm, V t, follows the geometric Brownian motion dv t V t = (µ δ) dt + σ db t, (2) where µ > δ is the instantaneous rate of return on assets, δ is the payout rate, σ is the instantaneous volatility and B t is a standard Brownian motion. With the tax-shield, the value of the firm is always larger than the value of the assets, V. Finally, the firm cannot sell assets to pay dividends, and the default-free term structure of interest rates is flat with a constant rate r per unit time. Default occurs when the asset value falls below an endogenously determined threshold. At that point, shareholders stop making the contractual payments to bondholders but keep control of the firm, servicing the debt strategically until the asset value returns above this threshold (strategic debt service). 18 In default, a bargaining game ensues between the firm s claimants. The parties will bargain over the total value of the firm, v(v ), which is divided according to the equilibrium outcome of a Nash bargaining game between shareholders and debt-holders. More specifically, if ṼS denotes the trigger point in asset value for which strategic debt service is initiated, for any V ṼS the firm value v(v ) is split between equity-holders and debt-holders as follows Ẽ(V ) = θv(v ), D(V ) = (1 θ)v(v ), (3) where Ẽ( ) and D( ) are the values of equity and debt, respectively, and θ is the sharing rule which maximizes the aggregate surplus of equity- and debt-holders in the following Nash bargaining 17 FS also consider extensions to allow for fixed liquidation costs and finite-maturity debt. We do not consider these extensions here to preserve analytical tractability while illustrating the basic intuition. 18 FS also consider a second type of exchange offer occurring during debt workouts, i.e., debt-equity swaps, in which shareholders offer debt-holders a fraction of the firm s equity in replacement of their original debt obligations and leave the control of the firm in the hands of debt-holders. While in the absence of taxes, the case of debtequity swap is equivalent to that of strategic debt service, in the presence of taxes strategic debt service is the dominating alternative since shareholders can capture the future tax benefits that are foregone in the debt-equity swap. We will, hence, limit our analysis to the case of strategic debt service.

14 12 game ] η [ θ = arg max [ θv(v ) 0 (1 θ)v(v ] 1 η ) (1 α)v ( ) (1 α)v = η 1. (4) v(v ) In the above game, η represents the bargaining power of shareholders and 1 η the bargaining power of bondholders. The shareholders surplus from bargaining is θv(v ) 0, because the alternative to bargaining is liquidation, in which case shareholders receive nothing. The bondholders surplus from bargaining is (1 θ)v(v ) (1 α)v, since the alternative entails a dissipative liquidation cost, α. As the equilibrium sharing rule (4) illustrates, shareholders receive more of the renegotiation surplus when their bargaining power η is higher and when the liquidation cost α is larger. The effect of bargaining power on the sharing rule is obvious. The role of liquidation costs is more subtle. The parameter α captures the loss of asset value that shareholders can potentially impose on creditors. This cost may be inflicted either through liquidation that occurs when negotiations fail or through the cost of legal battles in a bankruptcy court, or both. Hence, a high liquidation cost generates a stronger incentive for debt-holders to participate in the bargaining game, and thus indirectly increases shareholders bargaining power Valuation The valuation of claims follows standard techniques of contingent claim analysis (see, for example, Dixit and Pindyck (1994)). Proposition 3 in FS gives the following value for equity, Ẽ(V ) = θ v(v ) V c(1 τ) [ r + c(1 τ) (1 λ 1 )r λ 1(1 λ 2 )η (λ 2 λ 1 )(1 λ 1 ) ] ( ) λ1 τc Ṽ r if V > ṼS, V S if V ṼS,, (5)

15 13 where θ is the optimal sharing rule from the Nash bargaining game (4), ṼS is the endogenous level of asset values that triggers strategic debt service, Ṽ S = c(1 τ + ητ) r λ λ 1 1 ηα. (6) v(v ) is the total firm value, v(v ) = V + τc r λ 2 V + λ 1 τc λ 2 λ 1 r ( τc V λ 2 λ 1 r Ṽ ( S V Ṽ S ) λ1 if V > ṼS, ) λ2 if V ṼS,, (7) λ 1 = ( ) ( ) 2 ( ) ( ) r δ 1 σ 2 2 r δ σ + 2r < 0, and λ 2 σ 2 2 = 1 2 r δ + 1 σ 2 2 r δ σ + 2r > 1. 2 σ 2 From equation (5), the value of equity, when the firm is not in default (V > ṼS), is equal to its asset value V net of debt plus an adjustment term, which accounts for tax shields and the probability of default. 19 After renegotiation, the proceeds to equity-holders are given by θ v(v ) = η(v(v ) V ) + ηαv, following equation (4) for the optimal sharing rule θ. Since v(v ) V > 0, the proceeds θ v(v ) are hence increasing in the bargaining power η and liquidation costs α. Equity value and endogenous default threshold are increasing in bargaining power and/or liquidation costs (equations (5) and (6)). Both public bonds and bank debt usually come with covenants which require, at minimum, that the borrower honor the payment obligations specified in the debt contract. FS extend their bargaining model to consider the case in which hard cash flow covenants are in place. Under hard cash flow covenants, if the firm is not able to meet the contractual obligation on the debt, the debt-holders will take over or liquidate the firm. As FS show, the main effect of introducing hard cash flow covenants in a debt renegotiation model is to separate strategic default, which leads to bargaining in debt renegotiation, from liquidity default, that results in forced liquidations. Liquidity default triggered by hard cash flow covenants may be thought of as a special case of strategic default where shareholders have no bargaining power. 19 The quantity (V/Ṽ S ) λ 1 is the Arrow-Debreu price of a security that pays one dollar in the event that V ever reaches the threshold Ṽ S.

16 Equity returns and default probability For its empirical relevance, we are most interested in the connection between equity returns and default probability. In order to analyze this relationship, we need to derive both the expected returns on equity and the cumulative default probability implied by the above model. The closed-form expression for equity value in (5) is our starting point for deriving implications of the bargaining game for expected returns on equity. The quantity in the FS model that closely resembles the MKMV EDF measure is the probability of hitting the renegotiation boundary ṼS in (6) under the true probability measure governing the underlying process V. In the following proposition, we formally derive the expected returns and default probability implied by the FS model. Proposition 1 Under the assumptions of the FS model, the annualized t-period continuously compounded expected return on equity is given by r(0,t] E (V 0) = 1 ( t log E0 (Ẽ(V ) t)), (8) Ẽ(V 0 ) where E 0 (Ẽ(V t)), derived in equation (A3) of Appendix A, is the conditional expectation at t = 0 under the true probability measure of the asset value process in (2). The time 0 cumulative real default probability Pr (0,T ] over the time period (0, T ] is given by Pr (0,T ] (V 0 ) = N (h(t )) + ( V0 Ṽ S ) 2γ σ 2 N (h(t ) + 2γT σ T ), (9) with γ = µ δ 1 2 σ2 > 0, h(t ) = log( Ṽ S /V 0 ) γt σ T and N ( ) the cumulative standard normal function. Proof: See Appendix A. Equations (8) and (9) represent the theoretical counterparts of the empirically observed equity returns and default probability, respectively.

17 15 The model shows that shareholder advantage in default redistributes cash flows across the firm s claimants. This redistribution affects equity value and expected return. In addition, shareholder advantage, which is exogenous to the model, also impacts the default probability. Note that the risk profile of equity is affected through this cash flow channel and not through a missing default risk factor in the pricing kernel. By construction, the contingent claim model we use is silent about the pricing kernel which determines the value of the underlying assets in (2) Empirical implications The empirical analysis in Section 2 highlighted a complex relationship between default probability and equity returns. Given that we were able to obtain these two quantities explicitly within a plausible model of the default process, we can now analyze the implications of the model. As Proposition 1 illustrates, the link between expected returns and default probability is multi-dimensional, since both quantities are determined by a common set of variables and parameters. Instead of arbitrarily fixing a set of parameters and deriving an analytical relationship between expected returns and default probability, we simulate firms in the cross section by selecting different initial asset value V 0, coupon rate c, asset growth rate µ, and asset volatility σ, in order to match the distribution of these quantities in the data. We then compute the expected return and default probability for each firm, according to equations (8) and (9), respectively. Finally, we classify each firm in quintiles according to their default probability and, for each quintile, we report the equally-weighted expected return. Details of the simulations are contained in Appendix B. The main objective of this exercise is to highlight the role of the bargaining power coefficient η and of the liquidation cost coefficient α in determining how default probability and expected returns are related to each other. An important caveat to this exercise is that, since both 20 We do not examine in this paper the effect of shareholder advantage on bond prices which is discussed in Fan and Sundaresan (2000) and empirically explored in Davydenko and Strebulaev (2006). Note, however, that because debt renegotiation can be efficiency enhancing in the presence of liquidation costs, the benefits to shareholders do not necessarily come at the expense of bondholders. This intuition seems consistent with the evidence in Davydenko and Strebulaev (2006).

18 16 bargaining power and liquidation costs can potentially be endogenous variables, we cannot make a sensible causality statement about the relationship between default probability and equity returns. More specifically, since higher shareholders bargaining power can affect the payoff to lenders, it may affect the level and the terms of the firm s debt and, in turn, the probability of default itself. To fully account for such endogeneity, we would need to extend the model to consider the optimal capital structure decision, a worthy objective which is beyond the scope of the current paper. In the spirit of the Merton (1974) model which inspired the construction of the MKMV EDF measure, we instead take the debt level as given and analyze, in a partial equilibrium setting, the strategic effects of debt workout on equity returns. In Figure 1 we plot the simulated relationship between expected returns and default probability. The horizontal axis reports probability of default quintiles, while the vertical axis reports the annualized average returns on equity in each quintile. To match our empirical results, in the figure we take the horizon t for returns to be one month and the horizon T for the default probability to be one year. Panel A analyzes the effect of the bargaining power coefficient η on the relationship of interest while keeping the liquidation cost at a constant level (α = 0.5). Panel B, on the other hand, considers the effect of a changing level of liquidation cost α while assuming equal bargaining power (η = 0.5) between claimants. The left graph in Panel A shows the relationship between expected returns and default probability when shareholders have no bargaining power (η = 0), and default triggers immediate liquidation. In this case the relationship is monotonically increasing and explodes when default becomes certain, because shareholders are getting nothing in the event of default. Therefore, a higher probability of default is associated with higher risk to shareholders, and the liquidation cost does not play any role in either the default boundary or the default probability. Things change dramatically when shareholders have some bargaining power, as the right graph of Panel A demonstrates. The three sets of bars shown here refer to situations when shareholders have (i) low bargaining power (η = 0.2, darker bars); (ii) the same bargaining power as debt-holders (η = 0.5, middle bars); and (iii) high bargaining power (η = 0.8, lighter bars) Empirical evidence, e.g., Eberhart, Moore, and Roenfeldt (1990), finds that the amount recovered by shareholders in bankruptcy proceedings is usually less than 25% of the asset value. Since, in the absence of taxes, the

19 17 Figure 1: Default probability and expected returns For each decile of default probability within a year, the graph reports the average annual realized return obtained by simulating the FS model. We draw 50 values each of c, µ, and σ for a total of 125,000 firms. Simulation details are provided in Appendix B. The left figure in Panel A is obtained by assuming no bargaining power for shareholders, while the right figure in the same panel analyzes three different levels of bargaining power while fixing the liquidation cost at the level α = 0.5. Panel B reports the case of three different levels of liquidation costs while fixing the bargaining power at η = 0.5. Panel A: Effect of bargaining power η η = 0, any α α = η=0.2 η=0.5 η= Probability of Default Quintiles Probability of Default Quintiles Panel B: Effect of liquidation cost α η = α=0.2 α=0.5 α= Probability of Default Quintiles sharing rule θ in (4) is equal to η α, the choice of parameters η and α in Figure 1 implies that the share of asset received by shareholders in renegotiation for the bulk of our simulated firms is less than 25%.

20 18 Two patterns clearly emerge from this figure. First, in the presence of shareholder bargaining power, the relationship between equity return and default probability is hump-shaped, and for sufficiently high bargaining power, the relationship between expected return and default probability becomes downward sloping. This pattern is markedly different from the case of little or no shareholders bargaining power discussed above. Second, keeping everything else constant, high bargaining power is associated with low expected returns. The hump shape in the relationship is the result of the trade-off between the leverage effect of the debt and the de-leverage effect of shareholder advantage. At low levels of default probability, the likelihood of strategic renegotiation is remote. The leverage effect of debt determines the default risk of equity and leads to a positive relationship between default probability and expected returns. As the firm approaches the (endogenous) default boundary, shareholder advantage plays an increasingly important role. The benefits shareholders can extract in renegotiation with debt-holders reduce the effective leverage of equity. Hence, for firms with strong shareholder advantage, equity risk and expected returns decrease at high levels of default probability. In this case, default probability no longer captures adequately the equity risk associated with default. For sufficiently high shareholder advantage, this risk reduction effect dominates the leverage effect of debt even at low levels of default probability leading to a (mostly) downward sloping relationship. Panel B of Figure 1 demonstrates the relationship between default probability and expected returns as the level of liquidation costs changes while the bargaining power of claimholders is fixed at a common level η = 0.5. The three sets of bars represent the cases of (i) low liquidation costs (α = 0.2, darker bars); (ii) medium liquidation costs (α = 0.5, middle bars); and (iii) high liquidation costs (α = 0.8, lighter bars). The patterns emerging from this figure are similar to the ones obtained earlier by varying η for a given α, and the hump shape is now pervasive across all levels of liquidation costs. This is not surprising given that, in the solution of the optimal sharing rule (4) for the Nash bargaining game, the liquidation cost coefficient α enters with the same sign as the bargaining power coefficient η, and hence a larger liquidation cost has a similar effect as a larger shareholders bargaining power.

21 19 Our analysis so far suggests the following testable empirical predictions: Hypothesis 1 The relationship between default probability and expected returns should be (i) upward-sloping for firms with minimal shareholder advantage or (ii) hump-shaped and downward sloping for firms with substantial shareholder advantage. I.e., firms with weak shareholder advantage should exhibit a significantly different relationship from firms with strong shareholder advantage. Hypothesis 2 For a given default probability, expected returns should be lower for firms in which (i) shareholders have stronger bargaining power and/or (ii) the economic gains from renegotiation, i.e., liquidation costs, are larger. Hypothesis 2 is complementary to Hypothesis 1 and the implication of the latter can be used to refine the prediction of the former. In particular, since Hypothesis 1 implies a divergent behavior in the relationship between default probability and returns across firms with different levels of shareholder advantage, it also implies that the return difference between firms with strong and weak shareholder advantage predicted by Hypothesis 2 should be more pronounced at high levels of default probability when shareholders are more likely to effectively exercise their advantage. The discussion of cash flow-based covenants in Section allows us to further refine the above hypotheses. Since in the presence of binding cash flow-based covenants default triggers liquidation, the implication for the relationship between default probability and expected returns is qualitatively similar to the case of no shareholders bargaining power. This suggests that when cash flow-based covenants are binding, a positive relationship between default probability and expected returns is more likely. 4 Empirical analysis The theoretical argument presented above predicts that for firms in which shareholders are capable of obtaining a large advantage, expected returns are declining or hump-shaped in default

22 20 probability, while for firms in which shareholders are disadvantaged, a higher probability of default is associated with a higher probability of liquidation and hence a higher expected return. In this section we examine the consistency of these theoretical predictions in the data. 4.1 Data construction The model developed in the previous section identifies shareholder advantage as the result of shareholders bargaining power and liquidation costs. The first step in our empirical analysis is to construct reasonable proxies for these two theoretical concepts Shareholders bargaining power We use two proxies for shareholders bargaining power: (i) a firm s asset size and (ii) its ratio of R&D expenditure to assets. Small firms, because of information asymmetry, usually have a concentrated group of debtholders, mostly banks, which may have an advantage in monitoring the firm (see, e.g., Diamond (1991) and Sufi (2005)). This concentration of, and close monitoring by, creditors severely weakens shareholders bargaining power in the event of financial distress. Consistent with this notion, Franks and Torous (1994) and Betker (1995) find that firm size is a persistent determinant of deviation from the absolute priority rule for a sample of workouts and bankruptcies. In our test, we measure firm size by the market value of assets instead of the market value of equity for two reasons. First, this corresponds closely to the theoretical formulation, as the bargaining is over the remaining assets. Second, this can mitigate the potential bias caused by small equity values of firms close to bankruptcy even though they have a substantial asset base and a diffuse group of debt-holders. The market value of assets is obtained from MKMV and is available on a monthly basis. It is calculated, together with the EDF measure, as a function of the market value of equity, outstanding liability, and historical default data. We have also used the book value of assets from COMPUSTAT as an alternative measure of asset size and obtained qualitatively similar results, which are omitted here for brevity.

23 21 The second measure we use to proxy for shareholders bargaining power is the ratio of R&D expenditure to assets. As it has been documented in the literature, firms with high costs of research and development are particularly vulnerable to liquidity shortage in financial distress (e.g., Opler and Titman (1994)). This implies that these firms are more likely to encounter cash flow problems that can put them in a disadvantaged bargaining position with creditors. As discussed in Section 3.1.1, the presence of cash-flow based covenant precludes debt renegotiation and effectively reduce shareholders bargaining power to nil. In our test, the variable is calculated as a ratio of a firm s R&D expense (COMPUSTAT item #46) to the book value of assets. To allow time for accounting information to be incorporated into stock prices, we attribute the R&D ratio computed at the end of fiscal year t to the one-year period starting from July of year t Liquidation costs We use two proxies for liquidation cost: (i) the concentration of a firm s industry and (ii) the degree of tangibility of its assets. The existing literature suggests that the specificity of a firm s assets is important in determining a firm s liquidation value in bankruptcy (e.g., Acharya, Sundaram, and John (2005)). If a firm s assets are highly specific, or unique, then they are likely to suffer from fire-sale discounts in liquidation auctions (Shleifer and Vishny (1992)). This motivates us to choose the Herfindahl index, which captures the degree of industry concentration, as our first proxy for asset specificity. We use the Herfindahl index on sales, defined as I j Hfdl j = s 2 i,j, (10) i=1 where s i,j represents the sales of firm i as a fraction of the total sales in industry j, and I j is the number of firms belonging to industry j. 22 To compute the above quantity, at the end of each fiscal year t we first categorize firms according to the two-digit SIC code classification and 22 We have also used the Herfindahl index on asset values, which is constructed similarly, and obtained similar results.